Question: Solve for $x$ : $ 3|x + 3| + 6 = -1|x + 3| + 2 $
Answer: Add $ {1|x + 3|} $ to both sides: $ \begin{eqnarray} 3|x + 3| + 6 &=& -1|x + 3| + 2 \\ \\ { + 1|x + 3|} && { + 1|x + 3|} \\ \\ 4|x + 3| + 6 &=& 2 \end{eqnarray} $ Subtract ${6}$ from both sides: $ \begin{eqnarray} 4|x + 3| + 6 &=& 2 \\ \\ { - 6} &=& { - 6} \\ \\ 4|x + 3| &=& -4 \end{eqnarray} $ Divide both sides by ${4}$ $ \dfrac{4|x + 3|} {{4}} = \dfrac{-4} {{4}} $ Simplify: $ |x + 3| = -1$ The absolute value cannot be negative. Therefore, there is no solution.